IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v174y2024ics0304414924000863.html

Randomized limit theorems for stationary ergodic random processes and fields

Author

Listed:
  • Davydov, Youri
  • Tempelman, Arkady

Abstract

Using the randomization approach, introduced by A. Tempelman in Randomized multivariate central limit theorems for ergodic homogeneous random fields, Stochastic Processes and their Applications. 143 (2022), 89–105, we prove: (a) a randomized version of the invariance principle (the functional CLT); (b) a version the Glivenko–Cantelli theorem; (c) a randomized theorem about convergence of empirical processes to the Brownian bridge. We also weaken the moment condition in the randomized CLTs, proved in the mentioned article. The main point of our work is that most of our theorems are valid for all ergodic homogeneous random fields on Zm and Rm,m≥1.

Suggested Citation

  • Davydov, Youri & Tempelman, Arkady, 2024. "Randomized limit theorems for stationary ergodic random processes and fields," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000863
    DOI: 10.1016/j.spa.2024.104380
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924000863
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104380?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    2. Arkady Tempelman, 2022. "Randomized consistent statistical inference for random processes and fields," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 599-627, October.
    3. Na Zhang & Lucas Reding & Magda Peligrad, 2020. "On the Quenched Central Limit Theorem for Stationary Random Fields Under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2351-2379, December.
    4. Youri Davydov & Ričardas Zitikis, 2008. "On weak convergence of random fields," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 345-365, June.
    5. Tempelman, Arkady, 2022. "Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 89-105.
    6. Peligrad, Magda & Zhang, Na, 2018. "On the normal approximation for random fields via martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1333-1346.
    7. El Machkouri, Mohamed, 2002. "Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 285-299, December.
    8. Volný, Dalibor & Wang, Yizao, 2014. "An invariance principle for stationary random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4012-4029.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Na Zhang & Lucas Reding & Magda Peligrad, 2020. "On the Quenched Central Limit Theorem for Stationary Random Fields Under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2351-2379, December.
    2. Tempelman, Arkady, 2022. "Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 89-105.
    3. Magda Peligrad & Dalibor Volný, 2020. "Quenched Invariance Principles for Orthomartingale-Like Sequences," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1238-1265, September.
    4. Peligrad, Magda & Zhang, Na, 2018. "On the normal approximation for random fields via martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1333-1346.
    5. Steland, Ansgar, 2025. "Inference in nonlinear random fields and non-asymptotic rates for threshold variance estimators under sparse dependence," Stochastic Processes and their Applications, Elsevier, vol. 186(C).
    6. Lin, Han-Mai & Merlevède, Florence, 2022. "On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 198-220.
    7. Klicnarová, Jana & Volný, Dalibor & Wang, Yizao, 2016. "Limit theorems for weighted Bernoulli random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1819-1838.
    8. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    9. Johannes Krebs & Christian Hirsch, 2022. "Functional central limit theorems for persistent Betti numbers on cylindrical networks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 427-454, March.
    10. Hagemann, Andreas, 2019. "Placebo inference on treatment effects when the number of clusters is small," Journal of Econometrics, Elsevier, vol. 213(1), pages 190-209.
    11. Bai, Jushan & Han, Xu & Shi, Yutang, 2020. "Estimation and inference of change points in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 219(1), pages 66-100.
    12. Timothy Fortune & Magda Peligrad & Hailin Sang, 2021. "A local limit theorem for linear random fields," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 696-710, September.
    13. Hagemann, Andreas, 2025. "Inference on quantile processes with a finite number of clusters," Journal of Econometrics, Elsevier, vol. 249(PA).
    14. Steland, Ansgar, 2024. "Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    15. Victor Chernozhukov & Wolfgang K. Hardle & Chen Huang & Weining Wang, 2018. "LASSO-Driven Inference in Time and Space," Papers 1806.05081, arXiv.org, revised May 2020.
    16. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    17. Victor Chernozhukov & Ivan Fernandez-Val & Chen Huang & Weining Wang, 2024. "Arellano-bond lasso estimator for dynamic linear panel models," CeMMAP working papers 09/24, Institute for Fiscal Studies.
    18. Yizao Wang, 2014. "An Invariance Principle for Fractional Brownian Sheets," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1124-1139, December.
    19. repec:hum:wpaper:sfb649dp2017-026 is not listed on IDEAS
    20. Wang, Yizao & Woodroofe, Michael, 2014. "On the asymptotic normality of kernel density estimators for causal linear random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 201-213.
    21. Lahiri, S.N. & Robinson, Peter M., 2016. "Central limit theorems for long range dependent spatial linear processes," LSE Research Online Documents on Economics 65331, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000863. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.